Weighted dual functions for Bernstein basis satisfying boundary constraints

摘要

In this paper, we consider the issue of dual functions for the Bernstein basis which satisfy boundary conditions. The Jacobi weight function with the usual inner product in the Hilbert space are used. Some examples of the transformation matrices are given. Some figures for the weighted dual functions of the Bernstein basis with respect to the Jacobi weight function satisfying boundary conditions are plotted. We discuss special cases of the Jacobi weight function as the Legendre weight function and the Chebyshev weight functions of the first, second, and third kinds.